Dynamical sampling, derivatives, and interpolation formulas in the Paley--Wiener space

Iker Gardeazabal-Gutiérrez; Mateus Sousa

Dynamical sampling, derivatives, and interpolation formulas in the Paley--Wiener space

Classical Analysis and ODEs 2026-05-26 v2

Authors: Iker Gardeazabal-Gutiérrez , Mateus Sousa

Abstract

In this paper we present a criteria to obtain interpolations formulas in terms of the sequence $\left(\{T_n(f)(Nm)\}\}_{m\in\mathbb{Z}}\right)_{n=1}^N$ , where $f$ are functions whose Fourier transform is supported in $[-1/2,1/2]$ , and $T_n$ are certain Fourier multiplier operators. We also discuss applications and also prove that our results recover several classical formulas.

Keywords

interpolation theory interpolation fourier analysis

Cite

@article{arxiv.2506.16195,
  title  = {Dynamical sampling, derivatives, and interpolation formulas in the Paley--Wiener space},
  author = {Iker Gardeazabal-Gutiérrez and Mateus Sousa},
  journal= {arXiv preprint arXiv:2506.16195},
  year   = {2026}
}

Comments

23 pages - Changes: The main results of the paper now cover sets of stable sampling and not only interpolating sets

Dynamical sampling, derivatives, and interpolation formulas in the Paley--Wiener space

Abstract

Keywords

Cite

Comments

Related papers